24. Julia takes out a loan for \( \$ 1200 \) from a bank that charges \( 5.4 \% \) simple interest per year, If the total amount she repays is \( \$ 1297.20 \), for how long did she borrow the money?

To find out how long Julia borrowed the money, we can use the formula for simple interest: \[ A = P(1 + rt) \] where \( A \) is the total amount to be repaid, \( P \) is the principal amount (the initial sum), \( r \) is the interest rate, and \( t \) is the time in years. We know that: - \( A = 1297.20 \) - \( P = 1200 \) - \( r = 0.054 \) We need to find \( t \). Plugging in the known values into the formula, we have: \[ 1297.20 = 1200(1 + 0.054t) \] Dividing both sides by 1200 gives: \[ \frac{1297.20}{1200} = 1 + 0.054t \] Calculating the left side: \[ 1.081 = 1 + 0.054t \] Subtracting 1 from both sides: \[ 0.081 = 0.054t \] And now solving for \( t \): \[ t = \frac{0.081}{0.054} \approx 1.5 \] Julia borrowed the money for approximately 1.5 years, which is 18 months.